Engineering Economics
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Park2A1.pptxPark 2
Time Value of Money (Sections 2.1-2.3)
Interest: The Cost of Money
Money is a commodity, and like other goods that are bought and sold, money costs money.
Cost of money is established and measured by an interest rate, a percentage that is periodically applied and added to an amount of money over a specified length of time.
Interest is the cost of having money available for use.
The Time Value of Money
Money has both earning power (earning more money for its owner) and purchasing power (it can be put to work).
Since money has both of these, a dollar today has a higher value than a dollar received at some future time.
Interest versus inflation
Elements of Transactions Involving Interest
Principal (P): initial amount of money invested or borrowed in a transaction.
Interest rate (i): measures the cost or price of money and is expressed as a percentage per period of time.
Interest period (n): determines how frequently interest is calculated.
Elements of Transactions Involving Interest
Number of interest periods (N): a specified length of time that marks the duration of the transaction.
Plan for receipts or disbursements (An): yields a particular cash flow pattern over a specified length of time.
Future amount of money (F): results from the cumulative effects of the interest rate over a number of interest periods.
Methods of Calculating Interest
Simple Interest: interest earned on only the principal amount during each interest period.
I = (i*P) * N (interest earned)
F = P (1 + i * N) (future amount of money)
Compound Interest: interest earned in each period is calculated based on the total amount at the end of the previous period (includes original principle plus accumulated interest).
F = P ( 1 + i ) ^ N
Economic Equivalence
Economic equivalence refers to the fact that any cash flow can be converted to an equivalent cash flow at any point in time.
The present sum is equivalent in value to future cash flows because the present sum could be invested with interest and transformed into future cash flows.
F = P ( 1 + i ) ^ N
P = F ( 1 + i ) ^ -N
Interest Formulas for Single Cash Flows
Compound-Amount Factor
Given a present sum P invested for N interest periods at interest rate i, the future sum F will be the amount accumulated at the end of N periods:
Equation: F = P ( 1 + i ) ^ N
Factor Notation: P ( F/P , i , N)
Excel: = FV (i, N, 0, P)
Interest Formulas for Single Cash Flows
Present-Worth Factor
Finding the present worth of a future sum through the reverse of compounding (known as discounting process).
Equation: P = F ( 1 + i ) ^ -N
Factor Notation: F ( P/F, i, N)
Excel: = PV( i, N, 0, F)
Interest Formulas for Single Cash Flows
Solving for Time and Interest Rates
Solving for Interest
Trial and error, solve for i
Excel: = RATE(N, 0, P, F)
Solving for Time
Trial and error, solve for N
Excel: = NPER( i, 0, P, F)
